From dimensional analysis, the radius of the shock front \(R(t)\)  is known to increase with time \(t\)  as a power law \(R(t)\sim (E_0t^2/\rho _0)^{1/(d+2)}\)  in \(d\)  dimensions, where \(E_0\)  is the energy of the blast and \(\rho _0\)  is the ambient density of the system [1]}, [2]}, [3]}, [4]}, [5]}. This scaling law has been verified in many different contexts. The earliest and an accurate measurement was from the data of the Trinity nuclear explosion [1]}, [2]}. Later on, this scaling law has been verified experimentally in laser-driven blast waves in gas jets [8]}, plasma [9]}, or in atomic clusters of different gases [10]}.
